What is the ruling on a Muslim woman living in Western countries using "spirit vinegar" found in some ready-made foods such as mayonnaise and ketchup?

We do not know the composition of the materials mentioned. However, the Islamic legal principle is that foods and drinks made from pure ingredients are permissible (halal), based on general evidence from the Quran and Sunnah, such as the Almighty's saying: "O mankind, eat from whatever is on earth [that is] lawful and good," and His saying: "It is He who created for you all of that which is on the earth." However, if they are made from forbidden or impure ingredients, then they are unlawful (haram). If there is doubt about their ingredients, there is no impediment to using them unless the doubt reaches certainty or strong presumption.